Solving constant-coefficient differential equations with dielectric metamaterials

Recently, the concept of metamaterial analog computing has been proposed (Silva et al 2014 Science 343 160–3). Some mathematical operations such as spatial differentiation, integration, and convolution, have been performed by using designed metamaterial blocks. Motivated by this work, we propose a practical approach based on dielectric metamaterial to solve differential equations. The ordinary differential equation can be solved accurately by the correctly designed metamaterial system. The numerical simulations using well-established numerical routines have been performed to successfully verify all theoretical analyses.